Chiral algebras, factorization algebras and Borcherds’ “singular commutative rings” approach to vertex algebras
By Emily Cliff
In the late 1990s, Borcherds gave an alternate definition of some vertex algebras as "singular commutative rings" in a category of functors depending on some input data (A,H,S). He proved that for a certain choice of A, H, and S, the singular commutative rings he defines are indeed examples of vertex algebras. In this talk I will explain how we can vary this input data to produce categories of chiral algebras and factorization algebras (in the sense of Beilinson-Drinfeld) over certain complex curves X. We’ll discuss the failure of these constructions to give equivalences of categories and obstructions to extending this approach to more general varieties X.